Question 1087239

{{{-1}}},{{{-1/4}}},{{{-1/9}}},{{{-1/16}}},....... 

look for pattern:

 
{{{a[1]=-1}}}
{{{a[2]= -1(1/4)=-1(1/2^2)}}}
{{{a[3]= -1(1/9)=-1(1/3^2)}}}
{{{a[4]= -1(1/16)=-1(1/4^2)}}}

and for nth term will be:

{{{a[n] = -1/n^2}}} or {{{a[n] = -1(1/n^2)}}}where {{{n}}}={{{0}}},{{{1}}}, {{{2}}}...

by definition:
Sequences of numbers that follow a pattern of adding a fixed number from one term to the next are called arithmetic sequences.
The d-value can be calculated by subtracting any two consecutive terms in an arithmetic sequence.

{{{d = a[n] - a[n - 1]}}} where {{{n}}} is any positive integer greater than {{{1}}}

Sequences of numbers that follow a pattern of {{{multiplying}}} a fixed number,called the common ratio, from one term to the next are called geometric sequences.

{{{ a[n] = r[n]* a[n - 1]}}}

so, in your case we have geometric sequence because we multiplying fixed number {{{-1}}} by the common ratio {{{(1/n^2)}}}